I am just a student but we have had this topic recently.
One could say that there are many sentences in which you can use either the present perfect or the present perfect progressive.
Still there is a small differentation.
The present perfect is used to express the end of an action and its outcome whereas the present perfect progressive is used to express the duration of an action or its interception.
I have written five letters. -> outcome= five letters
I have been waiting for two hous. -> duration
I have done my homework-> I am now finished
I have been doing my homework -> It is not clear whether I am finished or still have to do sth.
On a German website I found out that there are some subdivisions when to use the pp or the ppp.
Outcome pp / Unpreferred byeffect ppp
Outcome pp: I have washed the car (it is clean now)
Byeffect: Why are you so wet? I have been washing the car.
Permanent pp /Momentarily ppp
Permanent:James has lived in London for ten years (He will live here for a while)
Momentarily: James has been living here for a year (It is clear that he won't stay here forever. Maybe he is just here for a school exchange?)
I hope I could help you
Best wishes Maluues
Student or Learner